Yingfu Xie wrote: > I had problems with an extension to a classic optimization problem. > > The target is to minimize a quadratic form a'Ma with respect to vector > b, where vector a=(b',-1)', i.e., a is the expand of b, and M is a > symmetric matrix (positive definite if needed). One more constrain on b > is b'b=1. I want to solve b given M. > > I tried but it seems impossible to find an analytic solution for b. Any > objection? > > Now, come to the numerical. Does anybody have any idea on how to > parameterize this to use, e.g. optim() or constrOptim()? > > Any help are appreciated very much!
The analytic solution is trivial. Write M as | M_11 c | | c' m | Then given that M_11 is positive definite, the minimizer is b = (M_11)^{-1}c cheers, Rolf Turner [EMAIL PROTECTED] ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.